A generalization of the Kuga-Satake construction

2005/03/07 by Claire Voisin, Voisin, Claire
Mathematics · Physics and Astronomy · #14C30 #14K10 #32G20 #Advanced Algebra and Geometry #Advanced Differential Geometry Research #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14C30 #msc:14K10 #msc:32G20

paper · pdf · doi:10.48550/arxiv.math/0503122

arxiv created 2005/03/07 · openalex publication_date 2005/03/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Kuga-Satake construction associates to a K3 type polarized weight 2 Hodge structure H an abelian variety A such that H is a quotient Hodge structure of H²(A). The first step is to consider the Clifford algebra of H. It turns out that it is endowed with a weight 2 Hodge structure compatible with the algebra structure. We show more generally that a weight 2 polarized Hodge structure which carries a compatible (unitary, associative) algebra structure is a quotient of the H² of an abelian variety.

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